# The exact value of tan ( π 3 ) .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter T, Problem 4DDT

(a)

To determine

## To find: The exact value of tan(π3).

Expert Solution

The exact value of tan(π3) is 3.

### Explanation of Solution

Result used:

The trigonometry result is tanx=sinxcosx.

Calculation:

The value of π3 is 60°.

Substitute π3=60° in the above mentioned result.

tan60°=sin60°cos60°=3212=32×2=3

Thus, the exact value of tan(π3) is 3.

(b)

To determine

### To find: The exact value of sin(7π6).

Expert Solution

The exact value of sin(7π6) is 12.

### Explanation of Solution

Result used:

The trigonometry result is sin(π+x)=sinx.

Calculation:

Use the above mentioned result and solve the exact value of sin(7π6) as follows,

sin(7π6)=sin(π+π6)=sin(π6)=12

Thus, the exact value of sin(7π6) is 12.

(c)

To determine

### To find: The exact value of sec(5π3).

Expert Solution

The exact value of sec(5π3) is 2.

### Explanation of Solution

Result used:

The trigonometry result is sec(2πx)=secx.

Calculation:

Use the above mentioned result and solve the exact value of sec(5π3) as follows,

sec(5π3)=sec(2ππ3)=sec(π3)=1cos(π3)=112

=2

Thus, the exact value of sec(5π3) is 2.

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