Question

What is the value of x?

sin(x+22)°=cos(2x−7)°

Remember to show all of you work for credit!





Given cosx=1213 and sinx=513 .

What is ratio for ​ tan x ​ ?

leave answer as a fraction in simplest form

Remember to show all of you work for credit!

Answer 1

Q1: Given sin(x+22)° = cos(2x−7)°

Using the concept of Right triangles and Trigonometric ratios, we can use a formula given as follows :-

If, sin(A) = cos(B). Then we must have A + B = 90 degrees.

We have sin(x+22)° = cos(2x−7)°

Then it must be true that (x+22)° + (2x−7)° = 90 degrees.

(x + 22) + (2x - 7) = 90

3x + 15 = 90

3x + 15 - 15 = 90 - 15

3x = 75

`(3x)/(3) =(75)/(3) \\\\x = 25 \;degrees`

Hence, x = 25 degrees is the final answer.

Q2: Given cos(x) = 1213 and sin(x) = 513.

It says to find ratio of tan(x).

Using the concepts of Trigonometric ratios, We can the formula that relates all three functions i.e. sin(x), cos(x), and tan(x).

tan(x) =
`(sin(x))/(cos(x))`

We can plug the given values in the formula.

`tan(x) = (513)/(1213)` is the final answer.