If cos 20=m determine the values of the following in terms of m. (a)sin 250 (b)sin 20 thanks
Reduce things to reference angles in Quadrant I:
sin 250 = sin(270-20) = -cos 20 = -m
since sin^2+cos^2 = 1,
sin 20 = √(1-m^2)
To find the values of sin 250 and sin 20 in terms of m, we can use the trigonometric identity: sin^2x + cos^2x = 1.
Given that cos 20 = m, we can solve for sin 20 as follows:
Step 1: Substitute cos 20 = m into the trigonometric identity.
sin^2 20 + (cos^2 20) = 1
Step 2: Rearrange the equation to solve for sin^2 20.
sin^2 20 = 1 - (cos^2 20)
Step 3: Substitute m for cos 20.
sin^2 20 = 1 - m^2
Step 4: Take the square root of both sides to find sin 20.
sin 20 = ± √(1 - m^2) -- (Note: taking the positive square root gives the principal value)
So, the value of sin 20 in terms of m is sin 20 = √(1 - m^2).
Next, let's find the value of sin 250.
Step 1: Use the trigonometric identity: sin(x + 180) = -sin(x).
sin 250 = sin (20 + 180)
Step 2: Substitute the value of sin 20 from the previous calculation.
sin 250 = sin (20 + 180) = -sin 20 = -√(1 - m^2)
Therefore, the values of sin 250 and sin 20 in terms of m are:
(a) sin 250 = -√(1 - m^2)
(b) sin 20 = √(1 - m^2)