Answer:
sqrt(1 - 36/49) = +root(13)/7
Step-by-step explanation:
sin^2t + cos^2t is identical to 1 for all t.
(6/7)^2 + cos^2t = 1
1 - 36/49 = cos^2t
hence plus/miuns sqrt(1 - 36/49) = cos(t)
since t is acute, the answer must be positive.
The value of cos t is √13/7.
Pythagorean identity is Pythagorean trigonometric identity which is derived by using Pythagoras Theorem to give relation between trigonometric function.
The basic Pythagorean identity for cosθ and sinθ is
sin²θ+cos²θ=1
So acoording to asked question,
t is the acute angle
sin t=6/7
So by using Pythagorean identity here
sin²t+cos²t=1
⇒cos t=√(1-sin²t)
⇒cos t=√(1-(6/7)²)
⇒cos t=√(1-36/49)
⇒cos t=√(49-36)/49
⇒cos t=√(13/49)
⇒cos t=±√13/7
As angle t is acute, the value of sin t and cos t will be positive.
⇒cos t=√13/7
Therefore the value of cos t is √13/7.
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