what is the value of sin(7π+30°)?
Answers
For angles less than a right angle, trigonometric functions are commonly defined as the ratio of two sides of a right triangle. The angles are calculated with respect to sin, cos and tan functions. Usually, the degrees are considered as 0°, 30°, 45°, 60°, 90°, 180°, 270° and 360°. Here, we will discuss the value for sin 30 degrees and how to derive the sin 30 value using other degrees or radians.
Sine 30 Degrees Value
The exact value of sin 30 degrees is ½. To define the sine function of an angle, start with a right-angled triangle ABC with the angle of interest and the sides of a triangle. The three sides of the triangle are given as follows:
The opposite side is the side opposite to the angle of interest.
The hypotenuse side is the side opposite the right angle and it is always the longest side of a right triangle
The adjacent side is the side adjacent to the angle of interest other than the right angle
The sine function of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side and the formula is given by:
sinθ=opposite sidehypotenuse side
Sine Law: The sine law states that the sides of a triangle are proportional to the sine of the opposite angles.
asinA=bsinB=csinC
The sine rule is used in the following cases :
Case 1: Given two angles and one side (AAS and ASA)
Case 2: Given two sides and non included angle (SSA)
The other important sine values with respect to angle in a right-angled triangle are:
Sin 0 = 0
Sin 45 = 1/√2
Sin 60 = √3/2
Sin 90 = 1
Answer:
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