Question

Find one value of θ or x that satisfies each of the following.sin θ = cos(2θ + 30°)

Accepted Answer

Recall the co-function identity in trigonometry: $$\sin 	heta = \cos(90^\circ - 	heta). $$This means we can rewrite the equation $$\sin 	heta = \cos(2	heta + 30^\circ) as$$ $$\sin 	heta = \cos(90^\circ - 	heta) to $$find a relationship between $$	heta$$ and $$2	heta + 30^\circ. $$Set the angles inside the cosine equal to each other using the identity: $$2	heta + 30^\circ = 90^\circ - 	heta. $$This gives an equation involving $$	heta$$ that you can solve. Solve the linear equation $$2	heta + 30^\circ = 90^\circ - 	heta by $$first adding $$	heta to $$both sides and subtracting $$30^\circ$$ from both sides to isolate $$	heta$$ terms on one side. Simplify the resulting equation to find the value of $$	heta. $$This will give you one possible solution for $$	heta$$ that satisfies the original equation. Remember that sine and cosine are periodic functions, so there may be multiple solutions. After finding one solution, consider the general solutions by adding the appropriate multiples of $$360^\circ or$$ $$2\pi$$ radians if needed.

Find one value of θ or x that satisfies each of the following.
sin θ = cos(2θ + 30°)

Verified video answer for a similar problem:

Key Concepts

Relationship Between Sine and Cosine Functions

Solving Trigonometric Equations

Angle Measures and Degree Conversion