Evaluate the expression. Assume that all angles are in Quadrant I.
14. tan(arccos 3/5)
=tan (cos^-1(3/5)
=tan(theta)
=4/3
To evaluate the expression 14 * tan(arccos(3/5)), we need to follow a step-by-step process.
Step 1: Find arccos(3/5)
- The arccos function (also known as the inverse cosine function) returns the angle whose cosine is equal to a given number. In this case, we want to find the angle whose cosine is equal to 3/5.
- To find arccos(3/5), use a scientific calculator or a trigonometric table. Alternatively, you can use a trigonometric identity:
arccos(x) = cos^(-1)(x)
So, arccos(3/5) = cos^(-1)(3/5)
Step 2: Evaluate cos^(-1)(3/5)
- Using a scientific calculator or trigonometric table, find the value of cos^(-1)(3/5).
- Let's assume it comes out to be x degrees.
Step 3: Evaluate tan(x)
- Now that we have the angle x, we can use the tangent function to evaluate tan(x).
- tan(x) is equal to the ratio of the sine of x to the cosine of x:
tan(x) = sin(x) / cos(x)
Step 4: Substitute the value of tan(x) in the expression
- We can replace tan(x) with the value obtained from step 3, in the expression 14 * tan(arccos(3/5)).
- So, the final result would be 14 * tan(x).
Keep in mind that the final answer will depend on the value of x we obtained in step 2, which is specific to the calculation of arccos(3/5).