Introduction to Trigonometry
expand_moreIntroduction to Trigonometry
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thumb_up thumb_downIntroduction to Triangles - Math Antics
expand_moreIntroduction to Triangles - Math Antics
Triangles aren't just mathematically significant, they are also fundamental to the way we build our environments, both physical and virtual. Triangles are special because they are exceptionally strong.
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thumb_up thumb_downUnderstand Triangles
- A triangle is a three-sided polygon. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees. Understanding triangles is very important in both Geometry and Trigonometry.
Classification of triangles
- Triangles can be classified by either their angles or sides.
Classification with angles
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An acute triangle is a triangle with all angles less than 90°.
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The right triangle is a triangle with 2 angles less than 90° and one angle equal to 90°.
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An obtuse triangle is a triangle with 2 angles less than 90° and one angle greater 90°.
Classification with sides
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An equilateral triangle is a triangle with all three sides equal to one another.
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An Isosceles triangle is a triangle with only two of the three sides equal to each other.
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A scalene triangle is a triangle with none of the three sides equal to one another.
In addition,
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The acute triangle can be Scalene, Isosceles, or Equilateral.
But, obtuse and right triangles can either be Scalene or Isosceles, never Equilateral.
Last but definitely not least
- The sum of any given triangle angles always adds up to 180°.
Pythagoras Theorem
expand_morePythagoras Theorem
Pythagoras theorem is used to find the length of a missing right-angle triangle side, when we have length of the other two sides, and the angle is not given.
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thumb_up thumb_downPythagoras theorem equation.
- a2+ b2 = c2 where:
- c - is the longest side of the right-angle triangle.
- a & b - can be any of the other two sides.
Used when the triangle is a right-angle triangle, the length of the two sides is given.
Trig ratios (SOH-CAH-TOA)
expand_moreTrig ratios (SOH-CAH-TOA)
There are six trigonometric ratios, Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent(Cot), Cosecant (Cosec), and Secant (Sec). However, for this section we going to focus on the three common ones (Sin, Cos, and Tan)
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thumb_up thumb_downName of each side of a right-angle triangle.
- Hypotenuse - The longer side of the right-angle triangle.
- Opposite - The side opposite the angle.
- Adjacent - the non-hypotenuse side that is next to a given angle
Trig ratios
- Sin (Angle A) = Opposite / Hypotenuse (SOH)
- Cos (Angle A) = Adjecent / Hypotenuse (CAH)
- Tan (Angle A) = Opposite / Adjacent (TOA)
SOH-CAH-TOA is used when the triangle is a right-angle triangle, the angle other than the right-angle is given, and a length of one side of that triangle .
Given the right angle triangle below, find the length of h if the length of a = 0 and b = 0.
Chances: 2
You get two chances for this question.
Now find the length of a if the length of b = 0 and h = 0.
Chances: 2
You get two chances for this question.
Given the right-angle triangle, find J if H = 0, and x = 0°.
✔️❌
Chances: 2
You get two chances for this question.
Now, Find the length of K
Your answer into two decimal places.
Chances: 2
You get a maximum of two chances for this question.
Find Angle HK, with your answer into zero decimal places.
✔️❌
Chances: 2
You get a maximum of two chances for this question.
- The first question you got 0/2
- The second question you got 0/2
- The third question you got 0/2
- The fourth question you got 0/2
- The fifth question you got 0/2
Your total is therefore, 0/0.
Percentage
%
A Message here
Trig ratio reciprocals
expand_moreTrig ratio reciprocals
Reciprocals of basic trigonometric ratios are the inverse values of the sin, cos, and tan values that are computed by reciprocating the sides required for computing the ratio.
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thumb_up thumb_downTrig ratio reciprocals
These include three extra ratios that are the reciprocals of the three basic trig ratios.
- Cosecant (Csc) is the reciprocal of sin. Therefore, Csc = 1/Sinθ
Csc = 1/Opposite/Hypotenuse
Use the rules for dividing fractions, which is to change the division sign to multiplication sign and flip the second fraction.
Csc = 1/1 * Hypotenuse / Opposite
everything multiplied by is itself
∴ Csc = Hypotenuse / Opposite -
Secant (Sec) is the reciprocal of cos. Therefore, Sec = 1/Cosθ
Sec = 1/Adjacent/Hypotenuse
Use the rules for dividing fractions, which is to change the division sign to multiplication sign and flip the second fraction.
Sec = 1/1 * Hypotenuse / Adjacent
everything multiplied by is itself
∴ Sec = Hypotenuse / Adjacent -
Cotangent (Cot) is the reciprocal of tan. Therefore, Cot = 1/Tanθ
Cot = 1/Opposite/Adjacent
Use the rules for dividing fractions, which is to change the division sign to multiplication sign and flip the second fraction.
Cot = 1/1 * Adjacent / Opposite
everything multiplied by is itself
∴ Cot = Adjacent / Opposite
The Sine Rule
expand_moreThe Sine Rule
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thumb_up thumb_downThe sine rule
- Used for nonright-angle triangles,
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When given two angles and one side opposite to one of the angles given,
- Or, when given two sides and one of the angle opposite one of the sides given.
Given a triangle below, Find BC when A = 0°, C = 0°, and AB = 0units
Your answer into two decimal places.
✔️❌
Chances: 2
You get a maximum of two chances for this question.
Given a triangle below, Find B when AB = 0units, AC = 0units, and C = 0°
Your answer into two decimal places.
✔️❌
Chances: 2
You get a maximum of two chances for this question.
Now, find the angle A.
✔️❌
Chances: 2
You get a maximum of two chances for this question.
- The first question you got 0/3
- The second question you got 0/2
- The third question you got 0/3
Your total is therefore, 0/0.
Percentage
%
A Message here
