For the given equation, solve for all values of (theta) to the nearest tenth of a degree. 2secant(theta)+10=0
2sec(theta) = -10
sec(theta) = -5
cos(theta) = - .2
take it from there
To solve the equation 2sec(theta) + 10 = 0 for theta, we need to isolate the secant function and then find its inverse. Here's how you can do it step-by-step:
Step 1: Subtract 10 from both sides of the equation:
2sec(theta) = -10
Step 2: Divide both sides of the equation by 2:
sec(theta) = -5
Step 3: Take the reciprocal of both sides:
cos(theta) = -1/5
Step 4: Use the inverse cosine function to find theta. The inverse cosine function is also known as arccosine and it gives you the angle whose cosine is a given value.
To find the principal angle (i.e., the angle between 0 and 180 degrees), use arccos(-1/5):
theta = arccos(-1/5)
Step 5: Use a calculator or online tool to find the arccos(-1/5) value. Rounding to the nearest tenth of a degree, we get:
theta ≈ 101.5 degrees
Therefore, the solution to the equation 2sec(theta) + 10 = 0 is theta ≈ 101.5 degrees (to the nearest tenth of a degree).