Finding The Angle In Radians

**1. In a circle with radius 12 cm, an arc of length 20 cm subtends a central angle of theta. Determine the measure of theta in radians.**

**Answer: 1.67 (Rounded to two decimals)**

My work:

(theta in radians) x Radius = arclength

(theta in radians) x 12 = 20

theta in radians = 20/12

Unsure how to continue...

**2. Solve: 7tan(x) = -3 0 <= x <= 2pi **

Answer: 2.74, 5.88 **(Rounded to two decimals)**

My work:

tan(x) = -3/7

3. For the function f(x) = 3sin(bx) + d, where b and d are positive constants, determine an expression for the smallest positive value of x that produces the maximum value of f(x)

Answer: pi/2b

How and Why?