An exact value for a trigonometric ratio is given
for each angle. Determine the exact values of
the other two primary trigonometric ratios.
a) sinθ _
3
5
, 0° ≤ θ ≤ 90°
To find the other two primary trigonometric ratios, we can use the Pythagorean identity:
sin^2θ + cos^2θ = 1
Given that sinθ = 3/5, we can solve for cosθ:
(3/5)^2 + cos^2θ = 1
9/25 + cos^2θ = 1
cos^2θ = 16/25
cosθ = ±4/5
Since 0° ≤ θ ≤ 90°, we take the positive value for cosθ:
cosθ = 4/5
To find the last primary trigonometric ratio, we can use:
tanθ = sinθ / cosθ
tanθ = (3/5) / (4/5)
tanθ = 3/4
So, the exact values of the other two primary trigonometric ratios are:
cosθ = 4/5
tanθ = 3/4