The value of sin60° × cos60° is :
Answers
Answer:
From the above equations, we get sin 60 degrees exact value as √3/2.
Step-by-step explanation:
Value of Sin 60 Degree
In a right-angled triangle, the sine of angle α is a ratio of the length of the opposite side(perpendicular) to the length of the hypotenuse side.
sin 60 degrees
Sin α= Opposite Side/Hypotenuse
=Perpendicular Side/Hypotenuse Side
= a/h
So, the ratio sin 60 degrees function will be, sin 60 = Perpendicular/Hypotenuse
There is a simple method by means of which we can calculate the value of sine ratios for all the degrees. If you learn this method, you can easily calculate the values for all other trigonometry ratios. So, let’s start with calculating the values for sin 0°, sin 30°, sin 45°, sin 60°, sin 90°.
Sin 0° = 0/4−−−√ = 0
Sin 30° = 1/4−−−√ = ½
Sin 45° = 2/4−−−√ = 1/√2
Sin 60° = 3/4−−−√ = √3/2
Sin 90° = 4/4−−−√ = 1
From the above equations, we get sin 60 degrees exact value as √3/2. In the same way, we can find the values for cos and tan ratios.
Therefore, the exact value of sin 60 degrees is √3/2
Cos 0° = Sin 90° = 1
Cos 30°= Sin 60° = √3/2
Cos 45° = Sin 45° = 1/√2
Cos 60° = Sin 30° =1/2
Cos 90° = Sin 0° = 0
Also,
Tan 0° = Sin 0°/Cos 0° = 0
Tan 30° = Sin 30°/Cos 30° =1/√3
Tan 45° = Sin 45°/Cos 45° = 1
Tan 60° = Sin 60°/Cos 60° = √3
Tan 90° = Sin 90°/Cos 90°= ∞
The above values of trigonometry ratios are with respect to degrees. We can also mention the values with respect to radians. Radians is considered for unit circle, whose radius is equal to one. The radian is denoted by π.
For 0°, the value of radian is 0. In the same way, we can create a table for trigonometry ratios with respect to π.
in 60 degrees.
Hey hyung
Hey hyunghope it helps...
sin 60=√3/2, cos 60 =1/2
sin60×cos60=√3/2×1/2
= √3/4
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