Definition of trigonometry
That branch of mathematics which deals with the relations of the sides and angles of triangles, which the methods of deducing from certain given parts other required parts, and also of the general relations which exist between the trigonometrical functions of arcs or angles.
Sine, cosine and tangent
The sine of an angle is the ratio, the length of the opposite side to the length of the hypotenuse. In our case
Sin A= opposite side/ hypotenuse
The cosine of an angle is the ratio, the length of the adjacent side to the length of the hypotenuse. In our case
Cos A= Adjacent side/ hypotenuse
The tangent of an angle is the ratio, the length of the opposite side to the length of the adjacent side. In our case
Tan A = opposite side/ adjacent side
Trigonometry Practice Problems:
Trigonometry practice problem- 1:
Simplify the following practice trigonometric expression.
Csc (x) sin (pi/2-x)
Solution:
Use the identity sin (pi/2-x) = cos(x) and simplify
Csc (x) sin (pi/2 –x) = csc (x) cos (x) =cot (x).
Trigonometry practice problem- 2:
Exact value of trigonometric functions:
Solve the exact value of sin (- Pi / 3).
Solution:
Do with the identity for negative angles, to write
sin (- Pi / 3) = - sin (Pi / 3)
Pi / 3 is in quadrant 1 and there is no need for either co terminal or reference angles. sin (- Pi / 3) is evaluated directly as follows.
sin (- Pi / 3) = - sin (Pi / 3) = - sqrt (3) / 2 .
Trigonometry practice problem- 3:
Trigonometric functions:
Here x is an angle in quadrant 3 and sin (x) = 1 / 3. Find sin (3x) and cos (3x).
Solution:
Do with the identity
sin (3x) = 3 sin x - 4 sin3x
= 3 (1/3) - 4 (1 / 3)3
= 23 / 27.
Sample Problems on Trignometry :
Trigonometry practice problem- 1:
Factor the following trigonometric expression.
Sin (x) + sin (2x).
Solution:
= sin x (1 + 2 cos x)
Trigonometry practice problem- 2:
Here x is in quadrant 3 and approximate sin (2 x) if cos (x) = - 0.2. Practice your answer with two decimal places.
Solution:
= 0.39
For more trigonometry problems you can Visit http://www.trigonometryhelp.org/trigonometry-practice-problems.html
That branch of mathematics which deals with the relations of the sides and angles of triangles, which the methods of deducing from certain given parts other required parts, and also of the general relations which exist between the trigonometrical functions of arcs or angles.
Sine, cosine and tangent
The sine of an angle is the ratio, the length of the opposite side to the length of the hypotenuse. In our case
Sin A= opposite side/ hypotenuse
The cosine of an angle is the ratio, the length of the adjacent side to the length of the hypotenuse. In our case
Cos A= Adjacent side/ hypotenuse
The tangent of an angle is the ratio, the length of the opposite side to the length of the adjacent side. In our case
Tan A = opposite side/ adjacent side
Trigonometry Practice Problems:
Trigonometry practice problem- 1:
Simplify the following practice trigonometric expression.
Csc (x) sin (pi/2-x)
Solution:
Use the identity sin (pi/2-x) = cos(x) and simplify
Csc (x) sin (pi/2 –x) = csc (x) cos (x) =cot (x).
Trigonometry practice problem- 2:
Exact value of trigonometric functions:
Solve the exact value of sin (- Pi / 3).
Solution:
Do with the identity for negative angles, to write
sin (- Pi / 3) = - sin (Pi / 3)
Pi / 3 is in quadrant 1 and there is no need for either co terminal or reference angles. sin (- Pi / 3) is evaluated directly as follows.
sin (- Pi / 3) = - sin (Pi / 3) = - sqrt (3) / 2 .
Trigonometry practice problem- 3:
Trigonometric functions:
Here x is an angle in quadrant 3 and sin (x) = 1 / 3. Find sin (3x) and cos (3x).
Solution:
Do with the identity
sin (3x) = 3 sin x - 4 sin3x
= 3 (1/3) - 4 (1 / 3)3
= 23 / 27.
Sample Problems on Trignometry :
Trigonometry practice problem- 1:
Factor the following trigonometric expression.
Sin (x) + sin (2x).
Solution:
= sin x (1 + 2 cos x)
Trigonometry practice problem- 2:
Here x is in quadrant 3 and approximate sin (2 x) if cos (x) = - 0.2. Practice your answer with two decimal places.
Solution:
= 0.39
For more trigonometry problems you can Visit http://www.trigonometryhelp.org/trigonometry-practice-problems.html
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