D. Find the values of the six trigonometric functions of 0 for the right triangle with the given sides. 8

Algebra & Trigonometry with Analytic Geometry
13th Edition
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Chapter6: The Trigonometric Functions
Section6.2: Trigonometric Functions Of Angles
Problem 22E
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D. Find the values of the six trigonometric functions of 0 for the right triangle with the given sides.
8
E. Given that 0 is an acute angle and cos 0 = 7/25, find
c) sec 0
a) tan 0
b) sin 0
F. Find the exact value of each expression.
a) csc 45° – sec 45°
b) csc 60° sec 30° + cot 45°
d) csc (T/6) – sec (T/3)
Transcribed Image Text:D. Find the values of the six trigonometric functions of 0 for the right triangle with the given sides. 8 E. Given that 0 is an acute angle and cos 0 = 7/25, find c) sec 0 a) tan 0 b) sin 0 F. Find the exact value of each expression. a) csc 45° – sec 45° b) csc 60° sec 30° + cot 45° d) csc (T/6) – sec (T/3)
H. Solve cach problem completely.
1. From the second-floor window directly across the street the angle of elevation of the top of an office
building in Makati is 57°20' and the angle of depression of the base is 18°16'. If the buildings are 38.3
meters apart, find the height of the office building.
2. The post office building in Manila is 21.8 meters away from the southern bank of the Pasig River. From a
window of the building 18.5 meters above the ground, a man finds that the angle of depression of the
northern bank is 8°12'. What is the width of the river at this point?
3. A plane flew 150 miles on a course of 220° and then 130 miles on a course 130°. Then the plane returned
to its starting point via the shortest route possible. Find that shortest distance.
I. Verify the following identities.
1. sin0+cotocos0 = csc0
3. sin 0(csc0-sin 0) = cos' 0
tan? 0 1-cos0
csc 0
2.
1+ tan? 0
= cot 0
4.
sec0 +1
coso
J. Determine the exact value by expressing the given angle in tems of the sum or difference of two special
angles.
(a) Cos 75°
(b) Csc165°
K. Use an addition formula to find the exact value of cos 15° cos 75° + sin 15° sin 75°
tan A = -3, A in QII
cotB = -/2, Bin QIV
L. Find sin (A + B), cos(A+B), and tan(A+B) if
M. Write sin 7x + sin 3x as a product.
N. Evaluate without using calculator.
a. -2 sin 52.5° sin 97.5°
b. cos 255° – cos 195°
O. Sketch the graph of y = -2sin (3x - n)
(tan)
P. Determine the exact value of csc
-1
cos
- cos
Transcribed Image Text:H. Solve cach problem completely. 1. From the second-floor window directly across the street the angle of elevation of the top of an office building in Makati is 57°20' and the angle of depression of the base is 18°16'. If the buildings are 38.3 meters apart, find the height of the office building. 2. The post office building in Manila is 21.8 meters away from the southern bank of the Pasig River. From a window of the building 18.5 meters above the ground, a man finds that the angle of depression of the northern bank is 8°12'. What is the width of the river at this point? 3. A plane flew 150 miles on a course of 220° and then 130 miles on a course 130°. Then the plane returned to its starting point via the shortest route possible. Find that shortest distance. I. Verify the following identities. 1. sin0+cotocos0 = csc0 3. sin 0(csc0-sin 0) = cos' 0 tan? 0 1-cos0 csc 0 2. 1+ tan? 0 = cot 0 4. sec0 +1 coso J. Determine the exact value by expressing the given angle in tems of the sum or difference of two special angles. (a) Cos 75° (b) Csc165° K. Use an addition formula to find the exact value of cos 15° cos 75° + sin 15° sin 75° tan A = -3, A in QII cotB = -/2, Bin QIV L. Find sin (A + B), cos(A+B), and tan(A+B) if M. Write sin 7x + sin 3x as a product. N. Evaluate without using calculator. a. -2 sin 52.5° sin 97.5° b. cos 255° – cos 195° O. Sketch the graph of y = -2sin (3x - n) (tan) P. Determine the exact value of csc -1 cos - cos
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