basic identities

Question

what is cosΘ when sinΘ= 2/5 ?

Answer 1

Hi Grace

I will assume you know what SOHCAHTOA stands for. The three sides of a right triangle are H - the hypotenuse (the long side, opposite the right angle; , O - the side opposite a given non-right angle, and A - the side adjacent to that angle.

If sin(theta) = 2/5, we know SOH - Sin = Opposite over Hypotenuse, so O = 2 and H = 5

We can find A by using the pythagorean formula: H^2 = A^2 +O^2 ------> 25 = A^2 + 4, or A =sqrt(21)

And, of course CAH - cos(theta) = Adjacent/Hypotenuse = A/H = sqrt(21) / 5

Answer 2

The sinθ = 2/5 indicates that y = 2 and the hypotenuse = 5. The x- value = √(5^2 - 2^2).

x = √(21).

The cosθ = √(21)/5 in the 1st quadrant or

cosθ = -√(21)/5 in the second quadrant.

Anita A.