Given that sinθ=0.3 and 0 is in the ​quadrant, what are cosθ and tanθ? Use the identity sin^2θ+cos^2θ=1 and the basic identities.

Question

Given that sinθ=0.3 and 0 is in the ​quadrant, what are cosθ and tanθ? Use the identity sin^2θ+cos^2θ=1 and the basic identities.

Answer 1

sinx = 0.3 = 3/10

cosx = square root of 1-sin^2x = sqr(1-9/100) = sqr(91/100)

=sqr91/10= about 0.954

tanx = sinx/cosx = (3/10)/(sqr91/10)

= 3/sqr91 = about 0.314

Answer 2

If θ is in the first quadrant, we know that both sin and cos are positive.

sin θ is given, and we have the identity sin(θ)² + cos(θ)² = 1

So, we can compute cos(θ) by taking the sqrt (1- (sin (θ))²)

Then, we use the formula for tan(θ) = sin(θ)/cos(θ)