Homework

Answer 1 To derive tan(a + b) in terms of tan(a) and tan(b), we start with the given identities for sin(a + b) and cos(a + b). Using the identity tan(x) = sin(x)/cos(x), we get tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a) * tan(b)).[yarpp...

Answer 1 The sine of a 30-degree angle in a right triangle is 0.5. This is derived from the ratio of the length of the side opposite the angle to the length of the hypotenuse. In a 30-60-90 triangle, the sides are in the ratio 1:√3:2, making the sine...

Answer 1 To find three consecutive integers whose sum is 93, let the integers be x, x+1, and x+2. Their sum is x + (x+1) + (x+2) = 93. Simplifying, we get 3x + 3 = 93. Solving for x, we find x = 30. Therefore, the three consecutive integers are 30,...

Answer 1 To find the amplitude and period of a transformed sine wave, use the general form y = A * sin(B(x - C)) + D. The amplitude is given by |A|, and the period is calculated as 2π / |B|. Here, A affects the amplitude, and B affects the...