Precalculus: Trigonometric Functions

Problem : Solve the following equation: cos(x) - tan²(x) = 1 .

Problem : Solve the following equation: 2 sec(x)sin³(x) = cos(x)tan²(x) .

Solution for Problem 2 >>

Resolving everything into sines and cosines and then cancelling, we have sin(x) = . x = , .

Close

Problem : Calculate cos(15) using the fact that cos(30) = .

Solution for Problem 3 >>

cos(15) = = .9659 .

Close

Problem : θ is in the first quadrant, and tan(θ) = . Find the sine, cosine, and tangent of 2θ .

Solution for Problem 4 >>

sin(θ) = . cos(θ) = . With these values, we can calculate sine, cosine, and tangent of 2θ . sin(2θ) = 2 sin(θ)cos(θ) 0.4283.cos(2θ) = cos²(θ) - sin²(θ) -0.9036.tan(2θ) = - 0.4740 .

Close

Problem : Express the following as a function of a single angle: .

Problem : Express the following as a sum or difference: cos(100)cos(50) .

Solution for Problem 6 >>

cos(100)cos(50) = (cos(100 + 50) + cos(100 - 50)) = (cos(150) + cos(50) .

Close

Problem : Simplify: sin²(x) + cos²(x) - sec²(x) + tan²(x) .

Problem : Solve: cos(x)tan(x) = csc²(x) - cot²(x) - 1 .

Solution for Problem 8 >>

x = {0,, Π,}

Close