Name: Sequential Trigonometry Trigonometry What does SOHCAHTOA stand for? opposite adjacent sin θ =
cosθ =
hypotenuse
tan θ =
hypotenuse
Date: opposite adjacent
What are the other three trigonometric functions? hyp hyp adj cscθ =
secθ =
cot θ =
opp
adj
opp
1. Evaluate the six trigonometric functions of angle K. Answer as decimals. sin(K) = __12/9 = 4/3___ csc(K) = ___3/4___ cos(K) = __9/15 = 3/5___ sec(K) = ___5/3___ tan(K) = _12/9 = 4/3___ cot(K) = ___3/4___
Two angles whose terminal sides coincide are called ____coterminal_____ angles. We find them by adding or subtracting ___360__º or ____2π___ radians. Find one p ositive and one negative angle that are coterminal w ith t he g iven a ngle. 2. 120° 3. −225° π
4.
5.
6
−240°, 480° −585°, 135° −
11π 13π ,
6
6
−
−
3π
4
11π 5π ,
4
4
Note: These are just two of an infinite number of angles coterminal with the given angle. There are many possible answers. An angle’s reference angle is the ___ positive, acute ___ angle between the terminal side and the x-­‐axis. Find the reference angle of the given angle. 6. 135º 45° 7. 330º 30° 8.
3π π
4 4
11π
6
9.
π
6
To convert between degrees and radians, use the fact that __180___º = ___2π___ radians. The units to cancel go in the __denominator____ Fraction on the calculator: MATH ENTER ENTER, then include ____π___ in your answer. Convert from degrees to radians or vise versa. 150º 5π
10.
6 300º 5π
11.
3 12.
2π
120° 3 13.
5π
225°
4 16.
⎛ 5π ⎞
1 sin ⎜ ⎟
⎝ 6 ⎠ 2
17.
⎛ 5π ⎞
1 cos ⎜ ⎟
⎝ 3 ⎠ 2
21.
secθ = 2 Evaluate the given trigonometric function. 14. sin225º 15. cos(30º) 3 2
−
2 2
Solve the trigonometric equations for 0º ≤ θ < 360º and for 0 ≤ θ < 2π. 18.
cosθ =
θ = 30°, 330° π 11π θ= ,
6 6
3
2
19.
cscθ = 2 θ = 45°, 135° π 3π θ= ,
4 4
20.
1
sin θ = − 2
θ = 60°, 300° θ = 210°, 330° θ=
θ=
7π 11π
,
6
6
For y = a sin(bx), the amplitude is ___a__ and the period is __ 2bπ __. Sine starts __at zero__, and cosine starts _up______ Graph one period of each of the following.
22. y = 3sin x 23. y = cos(2x) π/4 3π/4 π 5π ,
3 3