If tan o=7/24 and cos = 24/25then find sin.
Answers
Nanotechnology is the term given to those areas of science and engineering where phenomena that take place at dimensions in the nanometre scale are utilised in the design, characterisation, production and application of materials, structures, devices and systems.
Step-by-step explanation:
tep-by-step explanation:
Given : \tan\theta=\frac{24}{7}tanθ=
7
24
To find : \sin\theta+\cos \thetasinθ+cosθ ?
Solution :
\tan\theta=\frac{24}{7}tanθ=
7
24
According to trigonometry properties,
\tan\theta=\frac{P}{B}tanθ=
B
P
So, Perpendicular P=24 and Base B=7
The hypotenuse is H=\sqrt{P^2+B^2}H=
P
2
+B
2
H=\sqrt{24^2+7^2}H=
24
2
+7
2
H=\sqrt{576+49}H=
576+49
H=\sqrt{625}H=
625
H=25H=25
We know,
\sin\theta=\frac{P}{H}sinθ=
H
P
\sin\theta=\frac{24}{25}sinθ=
25
24
\cos\theta=\frac{B}{H}cosθ=
H
B
\cos\theta=\frac{7}{25}cosθ=
25
7
Substitute in the expression,
\sin\theta+\cos \theta=\frac{24}{25}+\frac{7}{25}sinθ+cosθ=
25
24
+
25
7
\sin\theta+\cos \theta=\frac{24+7}{25}sinθ+cosθ=
25
24+7
\sin\theta+\cos \theta=\frac{31}{25}sinθ+cosθ=
25
31