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le b. 51. Suppose that tan 0 = p/q, where p and q are positive ani 0° < 0 < 90°. Show that p sin0 q cos O p² – q° amtutmat p sin 0 + q cos 0 p² + q² +g² 52. This exercise shows how to obtain radical expressions for sin 15° and cos 15°. In the figure, assume that AB = BD = 2. %3D niwe 30° (a) In the right triangle BCD, note that DC = 1 because DC is opposite the 30° angle and BD = 2. Use the Pythagorean theorem to show that BC = V3. (b) Use the Pythagorean theorem to show that AD = 2\2 + V3. (c) Show that the expression for AD in part (b) is equal to V6 + V2. Hint: Two nonnegative quantities are 54. Thi %3D sin equal if and only if their squares are equal. (d) Explain why ZBAD = LBDA. (e) According to a theorem from geometry, an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles. Apply this to AABD with exterior angle DBC = 30°, and show that ZBAD = 15°. (f) Using the figure and the values that you have obtained for the lengths, conclude that (a (b 1 2 + V3 sin 15° cos 15° = Võ + V2 (c (g) Rationalize the denominators in part (f) to obtain Võ + V2 sin 15° cos 15° 4 4. (h) Use your calculator to check the results in part (g). 3. The following foure chows a regular eleven-sided polygon

le b. 51. Suppose that tan 0 = p/q, where p and q are positive ani 0° < 0 < 90°. Show that p sin0 q cos O p² – q° amtutmat p sin 0 + q cos 0 p² + q² +g² 52. This exercise shows how to obtain radical expressions for sin 15° and cos 15°. In the figure, assume that AB = BD = 2. %3D niwe 30° (a) In the right triangle BCD, note that DC = 1 because DC is opposite the 30° angle and BD = 2. Use the Pythagorean theorem to show that BC = V3. (b) Use the Pythagorean theorem to show that AD = 2\2 + V3. (c) Show that the expression for AD in part (b) is equal to V6 + V2. Hint: Two nonnegative quantities are 54. Thi %3D sin equal if and only if their squares are equal. (d) Explain why ZBAD = LBDA. (e) According to a theorem from geometry, an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles. Apply this to AABD with exterior angle DBC = 30°, and show that ZBAD = 15°. (f) Using the figure and the values that you have obtained for the lengths, conclude that (a (b 1 2 + V3 sin 15° cos 15° = Võ + V2 (c (g) Rationalize the denominators in part (f) to obtain Võ + V2 sin 15° cos 15° 4 4. (h) Use your calculator to check the results in part (g). 3. The following foure chows a regular eleven-sided polygon

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 40E
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le b. 51. Suppose that tan 0 = p/q, where p and q are positive ani 0° < 0 < 90°. Show that p sin0 q cos O p² – q° amtutmat p sin 0 + q cos 0 p² + q² +g² 52. This exercise shows how to obtain radical expressions for sin 15° and cos 15°. In the figure, assume that AB = BD = 2. %3D niwe 30° (a) In the right triangle BCD, note that DC = 1 because DC is opposite the 30° angle and BD = 2. Use the Pythagorean theorem to show that BC = V3.
Transcribed Image Text:le b. 51. Suppose that tan 0 = p/q, where p and q are positive ani 0° < 0 < 90°. Show that p sin0 q cos O p² – q° amtutmat p sin 0 + q cos 0 p² + q² +g² 52. This exercise shows how to obtain radical expressions for sin 15° and cos 15°. In the figure, assume that AB = BD = 2. %3D niwe 30° (a) In the right triangle BCD, note that DC = 1 because DC is opposite the 30° angle and BD = 2. Use the Pythagorean theorem to show that BC = V3.
(b) Use the Pythagorean theorem to show that AD = 2\2 + V3. (c) Show that the expression for AD in part (b) is equal to V6 + V2. Hint: Two nonnegative quantities are 54. Thi %3D sin equal if and only if their squares are equal. (d) Explain why ZBAD = LBDA. (e) According to a theorem from geometry, an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles. Apply this to AABD with exterior angle DBC = 30°, and show that ZBAD = 15°. (f) Using the figure and the values that you have obtained for the lengths, conclude that (a (b 1 2 + V3 sin 15° cos 15° = Võ + V2 (c (g) Rationalize the denominators in part (f) to obtain Võ + V2 sin 15° cos 15° 4 4. (h) Use your calculator to check the results in part (g). 3. The following foure chows a regular eleven-sided polygon
Transcribed Image Text:(b) Use the Pythagorean theorem to show that AD = 2\2 + V3. (c) Show that the expression for AD in part (b) is equal to V6 + V2. Hint: Two nonnegative quantities are 54. Thi %3D sin equal if and only if their squares are equal. (d) Explain why ZBAD = LBDA. (e) According to a theorem from geometry, an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles. Apply this to AABD with exterior angle DBC = 30°, and show that ZBAD = 15°. (f) Using the figure and the values that you have obtained for the lengths, conclude that (a (b 1 2 + V3 sin 15° cos 15° = Võ + V2 (c (g) Rationalize the denominators in part (f) to obtain Võ + V2 sin 15° cos 15° 4 4. (h) Use your calculator to check the results in part (g). 3. The following foure chows a regular eleven-sided polygon
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