Download 1.3 HW Worksheet

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Trigonometry 1.3 Homework
The terminal side of an angle with measure 𝜃 in standard position passes through the given point.
Sketch the reference triangle. Evaluate sin 𝜃, cos 𝜃 𝑎𝑛𝑑 tan 𝜃. Simplify all radicals.
1.) P (5, 12)
sin 𝜃 = ____________ cos 𝜃 = ____________ tan 𝜃 = ____________
2.) P ( -5, -12)
sin 𝜃 = ____________ cos 𝜃 = ____________ tan 𝜃 = ____________
3.) P (-6, -8)
sin 𝜃 = ____________ cos 𝜃 = ____________ tan 𝜃 = ____________
4.) P (6, 8)
sin 𝜃 = ____________ cos 𝜃 = ____________ tan 𝜃 = ____________
5.) P (10, -24)
sin 𝜃 = ____________ cos 𝜃 = ____________ tan 𝜃 = ____________
6.) P (-6, 4)
sin 𝜃 = ____________ cos 𝜃 = ____________ tan 𝜃 = ____________
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𝜃 is the measure of an angle in standard positon that lies in the given quadrant. When sin 𝜃 is given,
evaluate cos 𝜃 and tan 𝜃. When cos 𝜃 is given, evaluate sin 𝜃 and tan 𝜃. When tan 𝜃 is given, evaluate
sin 𝜃 and cos 𝜃. Simplify all radicals.
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7.)
sin 𝜃 =
8.)
tan 𝜃 = − 5 , 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼
9.)
tan 𝜃 =
10.)
cos 𝜃 = −
2
, 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼
3
4
5
, 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼
√2
2
, 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼
The terminal side of an angle with measure 𝜃 in standard position passes through the given point.
Sketch the reference angle. Evaluate sin 𝜃, cos 𝜃 𝑎𝑛𝑑 tan 𝜃. Simplify all radicals.
11.)
P (-12, 5)
12.)
P (3, -4)
13.)
P (5, 2)
2
𝜃 is the measure of an angle in standard position that lies in the given quadrant. Evaluate the other two
functions.
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14.)
cos 𝜃 = − 5 , 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼𝐼
15.)
tan 𝜃 = − 3 , 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝑉
16.)
tan 𝜃 = −1 , 𝑄𝑢𝑎𝑑𝑟𝑎𝑛𝑡 𝐼𝐼
4
𝜃 is the measure of an angle in standard position that lies in the given quadrant. In each blank write + or
– to indicate whether the values of the given functions are positive or negative in the given quadrant.
I
II
III
IV
17.)
𝑠𝑖𝑛𝜃
_____
_____
_____
_____
18.)
tan 𝜃
_____
_____
_____
_____
State the quadrant or quadrants in which an angle in standard positon with measure 𝜃 lies under the
given conditions.
19.)
𝑠𝑖𝑛 𝜃 < 0
20.)
cos 𝜃 < 0 𝑎𝑛𝑑 𝑠𝑖𝑛 𝜃 > 0
21.)
cos 𝜃 < 0 𝑎𝑛𝑑 𝑡𝑎𝑛 𝜃 > 0
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