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Chapter 6: Q. 19 (page 437)

find the value of the remaining five trigonometric functions of 蠎

sin蠎=57, 蠎 in Second Quadrant.

Short Answer

Expert verified

the value of the remaining five trigonometric functions of 蠎are:

cos蠎=-267tan蠎=-526cosec蠎=75sec蠎=-726cot蠎=-265

Step by step solution

01

Step 1. Given information

sin蠎=57,蠎 in Second Quadrant.

02

Step 2. Solving for  cosϑ

We know ;

sin2蠎+cos2蠎=1

Using this equation :

cos蠎=1-sin2蠎cos蠎=1-(57)2cos蠎=1-2549cos蠎=2449cos蠎=267

Since theta is in second quadrant so,

cos蠎=-267

03

Step 3. Solving forcotϑ , secϑ , cosecϑ

We know ;

cosec蠎=1sin蠎sec蠎=1cos蠎cot蠎=1tan蠎tan蠎=sin蠎cos蠎

Using the above identities :

tan蠎=-526cosec蠎=75sec蠎=-726cot蠎=-265

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Most popular questions from this chapter

Difference in Time of Sunrise Naples, Florida, is approximately 90 miles due west of Ft. Lauderdale. How much sooner would a person in Ft. Lauderdale first see the rising Sun than a person in Naples? See the hint. [Hint: Consult the figure. When a person at Q sees the first rays of the Sun, a person at P is still in the dark. The person at P sees the first rays after Earth has rotated so that P is at the location Q. Now use the fact that at the latitude of Ft. Lauderdale in 24 hours an arc of length 2蟺3559miles is subtended.]

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