2 條 sin cos tan

cosθ = 1/4
sin^2θ + cos^2θ = 1
sin^2θ = 1 - 1 / 16 = 15 / 16
so
5sin^2θ - 3cos^2θ
= 5 ( 15 / 16 ) - 3 ( 1 / 16)
= 75 / 16 - 3 / 16
= 72 / 16
= 4 . 5


2.
sin^2θ + cos^2θ = 1
cos^2θ = 1 - 1 / 25 = 24 / 25

so
4cos^2θ + 3sin^2θ
= 4 (24 / 25) + 3 (1 / 25)
= 96 / 25 + 3 / 25
= 99 / 25
= 3 . 96

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If cosθ = 1/4 find the value of 5sin^2θ - 3cos^2θ

5sin^2θ - 3cos^2θ
=5(1-cos^2θ)-3cos^2θ
=5-5cos^2θ-3cos^2θ
=5-8cos^2θ
=5-8(1/4)^2
=5-8(1/16)
=5-1/2
=9/2

If sinθ = 1/5 find the value of 4cos^2θ + 3sin^2θ

4cos^2θ + 3sin^2θ
=4(1-sin^2θ)+ 3sin^2θ
=4-4sin^2θ+ 3sin^2θ
=4-sin^2θ
=4-(1/5)^2
=4-1/25
=99/25

If cosθ = 1/4 find the value of 5sin^2θ - 3cos^2θ .
5 sin²θ - 3 cos²θ
= 5 ( 1- cos²θ ) - 3 cos ²θ
= 5 - 8 cos²θ
= 5 - 8 (1/4)²
= (10/2)- (1/2)
= 9 /2　or　= 4.5

If sinθ = 1/5 find the value of 4cos^2θ + 3sin^2θ .
4 cos²θ + 3 sin²θ
= 4 (1-sin²θ) + 3 sin ²θ
= 4 - sin²θ
= 4 - (1/5)²
= (100/25) - (1/25)
= 99/25　or　= 3.96

P.S. : use the formula　sin²θ + cos²θ =1