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

1. x = 55°

2. x = 11°

3. x = 30°

4. x = 19°

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}`