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If sin(t)=-\frac{1}{4} and t is in quadrant III then the value of cos(t) is AnswerIf your answer is not an integer then round it to the nearest hundredth.

If sin(t)=-\frac{1}{4} and t is in quadrant III then the value of cos(t) is AnswerIf-example-1
User China Syndrome
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2 Answers

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23 votes

Answer:

cos(t) = 0.94

Explanation:


{ \tt{ \sin(t) = - (1)/(4) }} \\ \\ { \tt{t = \sin ^( - 1) ( - (1)/(4) )}} \\ \\ { \tt{t = - 14.48}}

- therefore;

- A circle has four trigonometric quadrants;

  • quadrant I → All angles are positive
  • quadrant II → only sine angles are positive (180 - x)
  • quadrant III → only tangent angles are positive (180 + x)
  • quadrant IV → only cosine angles are positive (360 - x)

In the quadrant III, sine angles are negative;

- Since t is in the third quadrant;


{ \tt{ \tan(t) = \tan(14.48) }} \\ { \tt{ \tan(t) = 0.258}}

- Therefore;


{ \tt{ \tan(t) = ( \sin(t) )/( \cos(t) ) }} \\ \\ { \tt{ \cos(t) = ( - 0.25)/(0.26) }} \\ \\ { \tt{ \cos(t) = 0.94 }}

If sin(t)=-\frac{1}{4} and t is in quadrant III then the value of cos(t) is AnswerIf-example-1
User Artparks
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27 votes

ANSWER

Explanation: