This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems: 1. Find 135^ Step 1: Express 135^ using the sum of angles formula. We can write 135^ as 90^ + 45^. The sum identity for sine is (a+b) = a b + a b. 135^ = (90^ + 45^) Step 2: Apply the sum identity. (90^ + 45^) = 90^ 45^ + 90^ 45^ Step 3: Substitute the known values for the trigonometric functions. We know that 90^ = 1, 45^ = sqrt(2)2, 90^ = 0, and 45^ = sqrt(2)2. = (1)(sqrt(2)2) + (0)(sqrt(2)2) Step 4: Simplify the expression. = sqrt(2)2 + 0 = sqrt(2)2 The value of 135^ is sqrt(2)2. 2. Express 150^ in surd form. Step 1: Express 150^ using the sum of angles formula. We can write 150^ as 90^ + 60^. The sum identity for cosine is (x+y) = x y - x y. 150^ = (90^ + 60^) Step 2: Apply the sum identity. (90^ + 60^) = 90^ 60^ - 90^ 60^ Step 3: Substitute the known values for the trigonometric functions. We know that 90^ = 0, 60^ = (1)/(2), 90^ = 1, and 60^ = sqrt(3)2. = (0)((1)/(2)) - (1)(sqrt(3)2) Step 4: Simplify the expression. = 0 - sqrt(3)2 = -sqrt(3)2 The value of 150^ in surd form is -sqrt(3)2.