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-Inverses of the trigonometric functions. -How to use trigonometric ratios to solve for a missing side or angle of a right triangle.
Terms in this set (14)
How to find a missing length of an opposite side using sine ratio.
x = given angle
l = missing length
1) You are given an angle, and an adjacent side or hypotenuse. No opposite side.
2) Use sine ratio:
Sin∡x = opposite/hypotenuse
THEN
l = given side * sin∡x
(in scientific calculator)
l = sum of ^
How to find a missing angle using sine ratio.
x = missing angle
.123 = example sine
-Inverse sine always used when finding missing angles
1) You are given 2 sides. No 3rd side or angle.
2) Sin∡x =
opposite/hypotenuse
3) Sin∡x = .123
-DO NOT ROUND UNTIL END RESULT
4) x = inv sin (.123
5) x = ^
How to find missing length of a hypotenuse using sine ratio.
x = missing hypotenuse
o = example angle name
66 = example angle measure
17 = example opposite side
You are given an angle measure, and the length of the opposite side.
1) sin∡o = opposite/hypotenuse
2) sin 66 = 17/x
3) (x)(sin 66) = 17
4) (x)(0.9135454576) = 17
5) Divide both sides by sin66
(x)(0.9135454576) / (0.9135454576)
17 / (0.9135454576)
6) 17 / (0.9135454576)
7) x = 18.61
How to find a missing side using cosine.
100 = given side
cos 14 = given angle
p = missing side you're solving for
You are given an angle, and a side. Two missing sides, or one side and a hypotenuse are missing.
1) cos 14 = adjacent/hypotenuse
cos 14 = 100/p
2) Multiply both sides by p
p x cos 14 = p x cos 14
p x 100/p = 100
3) Then divide both sides by cos 14
p x cos 14 / cos 14
100 / cos 14
4) 100 / .9702957263
5) 103.06
How to find a missing angle using cosine.
x = missing angle
10 = example adjacent side
12 = example hypotenuse
You are given two sides. Angle is missing.
1) cos x = 10/12
2) cos x = .833
3) x = inv cos (.833)
4) x = 33.6
How to find missing height/side of a triangle using tangent.
h = missing height
300ft = example adjacent side
65 = example angle degree
You are given an angle, and an adjacent side. Opposite side and hypotenuse are missing.
1) tan = opp/adj
2) tan 65 = h/300 ft
3) h = 300ft x tan 65
4) h = 300 ft x 2.14
5) h = 643 ft
How to find missing angle using tangent ratio.
42 = example opposite side
55 = example angle
x = missing adjacent side
You are given opposite side, and angle. Adjacent side and hypotenuse are missing.
1) tan55 = 42/x
2) (x)(tan 55) = 42
3) (x)(1.428148007) = 42
4) (x)(1.428148007) / (1.428148007)
42 / (1.428148007)
5) x = 29.41
How to find missing angle using tangent ratio.
750 ft = example opposite side
1200 ft = example adjacent side
x = missing
You are given opposite side, and adjacent side. Hypotenuse and angle measure are missing.
1) tanx = 750ft/1200 ft
2) tanx = 0.625
3) x = inv tan (0.625
4) x = 32
Cosecant (csc)
Reciprocal of sine
csc = hypotenuse/opposite
Secant (sec)
Reciprocal of cosine
sec = hypotenuse/adjacent
Cotangent (cot)
Reciprocal of tangent
cot = adjacent/opposite
Trigonometric Functions
sin c = opposite/hypotenuse = 4/5
cos c = adjacent/hypotenuse = 3/5
tan c = opposite/adjacent = 4/3
Reciprocals
csc c = hypotenuse/opposite = 5/4
sec c = hypotenuse/adjacent = 5/3
cot c = adjacent/opposite = 3/4
Calculating Reciprocals
1 divided by the original trigonometric function
csc A = 1/sin A
sec A = 1/cos A
cot A = 1/tan A
Pythagorean Theorem for missing side
Use the given information and set up the desired trigonometric ratio.
If a side is missing, use the Pythagorean theorem to find it.
a^2 + b^2 = c^2
Use the third side to complete the desired trigonometric ratio.
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