How to solve this trig

Hi there!

To find the Trigonometric Equation, we have to isolate sin, cos, tan, etc. We are also given the interval [0,2π).

First Question

What we have to do is to isolate cos first.

Then find the reference angle. As we know cos(π/3) equals 1/2. Therefore π/3 is our reference angle.

Since we know that cos is negative in Q2 and Q3. We will be using π + (ref. angle) for Q3. and π - (ref. angle) for Q2.

Find Q2

Find Q3

Both values are apart of the interval. Hence,

Second Question

Isolate sin(4 theta).

Rationalize the denominator.

The problem here is 4 beside theta. What we are going to do is to expand the interval.

Multiply whole by 4.

Then find the reference angle.

We know that sin(π/4) = √2/2. Hence π/4 is our reference angle.

sin is negative in Q3 and Q4. We use π + (ref. angle) for Q3 and 2π - (ref. angle for Q4.)

Find Q3

Find Q4

Both values are in [0,2π). However, we exceed our interval to < 8π.

We will be using these following:-

Hence:-

For Q3

We cannot use any further k-values (or k cannot be 4 or higher) because it'd be +8π and not in the interval.

For Q4

Therefore:-

Then we divide all these values by 4.

Let me know if you have any questions!

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