The angle t is an acute angle and sin t is given. Use the Pythagorean identity sin^2t+cos^2t=1 to find cos t.

Question

sin t = √5/6

cos t = ____

Answer 1

To best answer your question, I'll use an example where sin t = √(2/3)

Please note that the answer at the end of this post is not equivalent to the answer of the original question.

sin² t + cos² t = 1

sin t = √(2/3)

Start by plugging in "sin t" to the equation:

[√(2/3)]² + cos² t = 1

Note that a square root cancels with the exponent 2 and simplify:

(2/3) + cos² t = 1

Subtract "(2/3)" from both sides to get "cos² t" by itself:

cos² t = 1 - (2/3)

Simplify by subtracting:

cos² t = (1/3)

Take the square root of both sides to find "cos t":

√(cos² t) = √(1/3)

Simplify "√(cos² t)":

cos t = √(1/3)

Simplify "√(1/3)":

cos t = (√3)/3

Final answer: cos t = (√3)/3