Calculate all trigonometric ratios for angle 30 degree and 60 degree geometrically
Answers
Step-by-step explanation:
To calculate the trigonometric ratios for angle 30 degree and 60 degree geometrically,
Draw an equilateral triangle,as all sides are equal and all angles are of 60°.
Now draw a perpendicular CD from opposite vertex C to the base AB.Since it Bisect the angle .
as we know that angle bisector bisect the side in Equilateral triangle,so
AB=BC=AC=k
AD=DB= k/2
Now in Triangle ADC,right angle at D, calculate the length of CD, by applying the Pythagoras theorem
CD= √3k/2
As we know that
sin A = CD/AC
here A = 60°
sin 60°=√3k/2/k=√3/2
cosec 60°= 2/√3
cos 60°=AD/AC= k/2/k= 1/2
sec 60°= 2 (reciprocal of cos 60°)
tan 60°= CD/AD= √3k/2/k/2=√3
cot 60°= AD/CD= 1/√3
By the same way in the same triangle
Find the value of sin 30°= AD/AC = 1/2
cosec 30°= 2
cos 30°=CD/AC= √3/2
sec 30°= 2/√3 (reciprocal of cos 60°)
tan 30°= AD/CD= 1/√3
cot 30°= CD/AD= √3
Hope it helps you.
Step-by-step explanation:
The value of sin 30 degrees is 0.5. Sin 30 is also written as sin π/6, in radians. The trigonometric function also called as an angle function relates the angles of a triangle to the length of its sides. Trigonometric functions are important, in the study of periodic phenomena like sound and light waves, average temperature variations and the position and velocity of harmonic oscillators and many other applications. The most familiar three trigonometric ratios are sine function, cosine function and tangent function.
Sine 30°=1/2
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.