question on trigonometry 3 equations
I'm sorry, I cannot answer your question without further information. Can you please provide the three equations related to trigonometry?
solve the equation 2sin^2( x -30) =cos60degrees for -180<x<180 degrees
2)solve the equation 6cos^2x+7sinx-8=0 for 0 degrees <x<90 degrees
3)determine the amplitude and period of the function y=2 cos(3x-45)degrees
4)determine the amplitude and the period of the function Y=3sin(2x+40)degrees
5)solve the equation sin(2t+10)degrees=0.5for0degrees<t<180degrees
1)
2sin^2(x-30) = cos60
2sin^2(x-30) = 1/2
sin^2(x-30) = 1/4
sin(x-30) = ± 1/2
x-30 = 30 + 180n or x-30 = 150 + 180n (n is an integer)
x = 60 + 180n or x = 180 + 180n or x = 210 + 180n
2)
6cos^2x + 7sinx - 8 = 0
6(1-sin^2x) + 7sinx - 8 = 0
6sin^2x - 7sinx + 2 = 0
(2sinx - 1)(3sinx - 2) = 0
sinx = 1/2 or sinx = 2/3
x = 30 + 360n or x = arcsin(2/3) ≈ 41.81°
3)
Amplitude: 2
Period: 2π/3
4)
Amplitude: 3
Period: π
5)
sin(2t+10) = 0.5
2t+10 = arcsin(0.5) + 360n or 2t+10 = π - arcsin(0.5) + 360n (n is an integer)
2t+10 = 30 + 360n or 2t+10 = 150 + 360n
t = 10 + 180n or t = 70 + 180n