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Chapter 6: Q. 10 (page 435)

Find the exact value of each expression. Do not use a calculator.

cos540鈭�-tan(-405鈭�)

Short Answer

Expert verified

The value of the given expression is 0.

Step by step solution

01

Step 1. Given

Given trigonometric function

cos540鈭�-tan(-405鈭�)

02

Step 2. Concept

We will use standard formula of sin胃 and cos胃 at different angles for calculating the final result of given expression.

03

Step 3. Calculation of cos540∘

We know

cos360+胃=cos胃thus,cos(360+180)=cos(540)cos(180)=-1

04

Step 4. Calculation of tan(-405∘)

We know

tan(360+45)=tan45Alsotan(-45)=-tan(45)therefore,tan(-405)=-1

05

Step 5. Final calculation

Substituting the values of trigonometric expression we get

cos540-tan(-405)=-1-(-1)=-1+1=0

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Most popular questions from this chapter

In the problem, sdenotes the length of the arc of a circle of radius r subtended by the central angle 胃. Find the missing quantity. Round answers to three decimal places.

胃=13radian, s=2 feet , r=?

the point (x, y) is on the terminal side of angle in standard position. Find the exact value of the given trigonometric function

(6,-3),tan蠎

find the value of the remaining five trigonometric functions of 蠎

role="math" localid="1646316653225" cos蠎=233蟺2<蠎<2蟺

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

210掳

In problems 13-20, Px,yis the point on the unit circle that corresponds to a real number t. Find the exact values of the six trigonometric functions of t.

223,-13.
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