Question
Use the information given about the angle
, to find the exact values of the foliowing.
Ask by Vargas Donnelly. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
To solve the problem, we start with the known condition
and the range
. This indicates that
is in the second quadrant.
Step 1: Find
Using the Pythagorean identity:
Substituting the value of
:
Taking the square root, since
is positive in the second quadrant:
Step 2: Calculate
and
Using the double angle formulas:
(a) Calculate
:
(b) Calculate
:
Step 3: Calculate
and
Using the half-angle formulas:
© Calculate
:
(d) Calculate
:
Final Answers
- (a)
- (b)
- ©
- (d)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg


Beyond the Answer
To find
and
, we start from the given cosine value
. Since
,
is in the second quadrant, which means
is positive.
Using the Pythagorean identity:
we can solve for
:
Now we can find the half-angle values. Using half-angle formulas:
Next, we also need
:
So, putting it all together: