Analytical Trigonometry Exercises

Example 1

Solve 2cos θ = 1 for

Hint

One angle that makes .

Example 2

Solve .

Hint

Convert to cot^-1's reciprocal, .

Example 3

Solve 2sin² θ – sin θ = 1 for .

Hint

sin² θ is the same as (sin θ)². Factor, then solve. There are 3 solutions between 0 and 2π. One angle is on an axis, and the others are in Quadrants III and IV.

Example 4

Solve .

Hint

Wait until the very end to divide out the 2 from θ. Also, don't forget to find the equivalent reference angle in Quadrant IV.

Example 5

Solve 2sin (2θ) + 1 = 0 for .

Hint

If this were 2sin θ + 1 = 0, then the two angles between 0 and 2π that would satisfy this equation would be and . But that's not the equation we have to solve here. Too bad, so sad.

Analytical Trigonometry Exercises

Example 1

Example 2

Example 3

Example 4

Example 5

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