Thread: trigonometric functions

Math trigonometric questions?

1)Determine tan2θ if sinθ + cosθ = -1

2) Express sin2θ in terms of csc θ and sec θ

3) Express cos3θ in terms of sin θ

Originally Posted by crosser43

Math trigonometric questions?

1)Determine tan2θ if sinθ + cosθ = -1

2) Express sin2θ in terms of csc θ and sec θ

3) Express cos3θ in terms of sin θ

1) sinθ + cosθ = -1
sinθ + cosθ + 1 = 0
2sin(0.5θ)cos(0.5θ) + 2cos^2(0.5θ) = 0
2*cos(0.5θ)[sin(0.5θ) + cos(0.5θ)] = 0
cos(0.5θ) = 0 or 0.5θ = 0.5π or θ = π
sin(0.5θ) + cos(0.5θ) = 0
tan(0.5θ) = -1 or 0.5θ = 0.25π or 2θ = π

Hello crosser43

Originally Posted by crosser43

Math trigonometric questions?

1)Determine tan2θ if sinθ + cosθ = -1

Square both sides:





Now use the identities and :

2) Express sin2θ in terms of csc θ and sec θ

3) Express cos3θ in terms of sin θ

See line 40 of Multiple-Angle Formulas -- from Wolfram MathWorld, and put

Grandad