Chapter 10 - NCPN

When Trigonometric Function Values Are Positive
• The sine function is positive for angles in
Quadrants I and II.
• The cosine function is positive for angles in
Quadrants I and IV.
• The tangent function is positive for angles in
Quadrants I and III.
Example 2
Using the Half-Angle Identity
At the beginning of this lesson, a situation was presented in which a
transmitter at the radio station needed to evaluate sin 150° to isolate a radio
frequency. What is the isolated frequency Use a half-angle identity to find
the exact value of sin 150°.
Solution
Because cos 300° = 1 2 , the identity sin
the exact value of sin 150°.
cos
sin
A 1−
A
= ±
2 2
cos
sin
300°
1− 300°
= ±
2
2
A
= ±
2
1−
cos A
can be used to find
2
Choose the positive square root since sin 150° is positive.
sin
300°
= ±
2
sin
300°
= ±
2
sin
300°
= ±
2
sin
300°
= 1 2 2
1−
1 2
2
1
2
2
1
4
The exact value of sin 150° is 1 2 . So the isolated frequency is 1 2 .
Ongoing Assessment
Use a half-angle identity to find the exact value of tan 150°. − 3
3
10.8 Double-Angle and Half-Angle Identities 481