How do I solve Cos(theta)= 3/7 if 0 degrees is less than or equal to theta and theta is less than or equal to 90 degrees?
You know the cosine is positive in quadrants I and IV
so take the inverse cosine of 3/7
My calculator gave me 64.62 degrees.
Since you only wanted the angle in the first quadrant, that's all.
To solve the equation cos(theta) = 3/7, where 0 degrees is less than or equal to theta and theta is less than or equal to 90 degrees, you can follow these steps:
Step 1: Understand the problem.
The equation cos(theta) = 3/7 represents the ratio of the length of the adjacent side to the hypotenuse in a right-angled triangle, where theta is one of the acute angles.
Step 2: Use the inverse cosine function.
To find theta, you need to use the inverse cosine function or arccosine function denoted as cos^(-1) or arccos. This function will give you the angle for a given cosine value.
Step 3: Calculate the angle.
By taking the inverse cosine of both sides of the equation, you get:
theta = cos^(-1)(3/7).
Step 4: Evaluate the angle.
Using a calculator or a table of values, find the angle whose cosine is 3/7.
theta ≈ 66.42 degrees.
Therefore, the solution to the equation Cos(theta) = 3/7, where 0 degrees is less than or equal to theta and theta is less than or equal to 90 degrees, is theta ≈ 66.42 degrees.