Learn Trigonometry Test Questions

Introduction to learn trigonometry test questions:
Here we are going to see the article as learn trigonometry test questions, generally trigonometry is used to study about the triangle especially right angle triangle ,the main purpose of trigonometry is  used to find the sides and angle of a right angle triangle with the help of a trigonometric functions  such as sin ,cos, tan ,secant ,cosecant and cot. Let us start to learn some of the trigonometry test questions.


Example 1-learn trigonometry test questions:

Suppose A and B are positive acute angles and the value of cos A = `12/15` , and sin B =` 8/10` , what is the value of Sin (A + B)?

Solution:

`cos A = 12/15` , from that we find the value of sin A

Already we know that the `cos A= (adjacent side)/("hypotenuse") `

So adjacent is 12 and hypotenuse is 15

Use the Pythagorean Theorem here to find the unknown side it will be shown in below,

`(Opposite side)^ 2= ("hypotenuse")^ 2- (adjacent)^2 `

So adjacent is 12 and hypotenuse is 15

`"= (15)^2-(12)^2=225-144=81=9^2`

Opposite side =9

So `sinA =(opposite side)/("hypotenuse") `

The value of `sin A is 9/15`

Similarly

`sin B = 8/10` , from that we find the value of sin B

Already we know that the `sin B = (opposite side)/("hypotenuse") `

So opposite side is 8 and hypotenuse is 10 now use the Pythagorean Theorem to find the adjacent values

`(Adjacent side)^2 ` `= (10)^2-(8)^2=100-64=36=6^2`

So the value of adjacent side is `6/10`

`cos B=6/10`

`"cos A = 12/15, sin B=8/10, sin A =9/15, cos B = 6/10`


sin (A+B) = sinAcosB + cosAsinB
sin (A+B)= `(9/15) xx (6/10) + (12/15) (8/10)`

sin (A+B)= `(54/150) + (96/150) =1`

Example 2-learn trigonometry test questions:

Suppose the adjacent side of a right angle triangle is 6cm and opposite side of a triangle is 8cm find the hypotenuse of a triangle?

Solution:

Here the adjacent side of a right angle triangle is given as 6cm and opposite side of a right angle triangle is given as 8cm

We know that formula for Pythagorean Theorem

`AC^2=AB^2+BC^2`

Here AC is the hypotenuse

AB is the opposite side and BC is the adjacent side of a triangle

Plug those values in the above formula means we get the hypotenuse value

`AC^2=6^2+8^2`

`AC^2=36+64=100`

`AC^2= (10)^2`

So the value of hypotenuse is 10cm

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Some of the trigonometry test questions with the answer key:


                 `"sin^3A+cos^3A `
1) prove   _______________     = 1- sin A Cos A
                    sin A + cos A

2)Suppose the opposite side of a right angle triangle is 15cm and hypotenuse of a triangle is 17cm find the adjacent side of a triangle?

Answer:

8cm