Question

PLEASE HELP! SHOW WORK AND/OR EXPLANATION PLEASE.
Find ‘x’ that will make the following statements true.

1. Sin (35) = Cos (x)
2. Cos (79) = Sin (x)
3. Cos (x) = Sin (2x)
4. Sin (x + 4) = Cos (4x – 9)

Answer 1

Answer:

1.  x = 55°

2.  x = 11°

3.  x = 30°

4.  x = 19°

Step-by-step explanation:

Trigonometric Identities

$\sin(x)=\cos(90^{\circ}-x)$

$\cos(x)=\sin(90^{\circ}-x)$

Question 1

$\begin{aligned}\implies \sin(35) & =\cos(90-35)\\ & = \cos(55)\end{aligned}$

$\implies x=55^{\circ}$

Question 2

$\begin{aligned}\implies \cos(79) & =\sin(90-79)\\ & = \sin(11)\end{aligned}$

$\implies x=11^{\circ}$

Question 3

$\begin{aligned}\cos(x)& =\sin(2x)\\\implies \cos(x)& =\sin(90^{\circ}-x)\\\\\implies 2x & = 90-x\\3x & = 90\\x & = 30^{\circ}\end{aligned}$

Question 4

$\begin{aligned}\sin(x+4)& =\cos(4x-9)\\\implies \sin(\theta)& =\cos(90^{\circ}-\theta)\\\\\implies x+4 & = 90-(4x-9)\\x+4 & = 90-4x+9\\5x & = 95\\x & = 19^{\circ}\end{aligned}$