PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Chapter 5.5, Problem 49E
To determine

To find:The exact values of the sine, cosine and tangent at angle 75° using half-angle formula.

Expert Solution & Answer
Check Mark

Answer to Problem 49E

The exact values of the sine, cosine and tangent at angle 75° are 2+32 , 232 and 2+3 , respectively.

Explanation of Solution

Given information:

The given angle is 75° .

Calculation:

Let the given angle is 75° and it is half of angle 150° . Since, angle 75° lies in Quadrant I. So, the values of sine, cosine and tangent will be positive.

Write the expression to calculate the value of sin75° .

  sin75°=±1cos150°2=±1(32)2 {cos150°=32}

Since, the value of sine is positive in Quadrant I. So, consider the positive value and simplify it.

  sin75°=1(32)2=2+32×2=2+32

Write the expression to calculate the value of cos75° .

  cos75°=±1+cos150°2=±1+(32)2 {cos150°=32}

Since, the value of cosine is positive in Quadrant I. So, consider the positive value and simplify it.

  cos75°=1+(32)2=232×2=232

Similarly, write the expression to calculate the value of tan75° .

  tan75°=1cos150°sin150°=1(32)(12) {cos150°=32sin150°=12}

Since, the value of tangent is positive in Quadrant I. So, consider the positive value and simplify it.

  tan75°=1(32)(12)=(2+32)(12)=2+3

Therefore, the exact values of the sine, cosine and tangent at angle 75° are 2+32 , 232 and 2+3 , respectively.

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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How to apply the law of sines to find the remaining parts of a triangle; Author: Brian McLogan;https://www.youtube.com/watch?v=NdRF18HWkmE;License: Standard YouTube License, CC-BY