Practice: Basic Trigonometric Identity

Geometry Level 1

What is the value of sin 2 0 + cos 2 9 0 \sin^2 0 ^ \circ + \cos ^2 90 ^ \circ ?


The answer is 0.

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17 solutions

sin 0 = 0 sin 2 0 = 0 2 = 0 \sin 0 = 0\ \Rightarrow\ \sin^2 0 = 0^2 = 0

cos 9 0 = 0 cos 2 9 0 = 0 2 = 0 \cos 90^\circ = 0\ \Rightarrow \ \cos^2 90^\circ = 0^2 = 0

0 + 0 = 0 0 + 0 = \boxed{0}

0

Rahman Ali - 7 years, 5 months ago
Budi Utomo
Dec 23, 2013

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 Yeah, the solution is zero. -_- ...... ;-)

0

Shubhadeep Roy - 7 years, 2 months ago
Rahul Saha
Dec 23, 2013

We know, s i n ( x ) = c o s ( 90 x ) sin(x)=cos(90-x)

Therefore, s i n 2 ( 0 ) + c o s 2 ( 90 ) = 2 c o s ( 90 ) = 0 sin^2(0)+cos^2(90)=2\cdot cos(90)=0

This is mosquito-nuking,really.Just figure out the values of s i n ( 90 ) sin(90) and c o s ( 90 ) cos(90) individually and plug them in.

Vishnudatt Gupta
May 2, 2014

sin 0=0; sin^2 0=0

cos 90=0 cos^2=0

0+0=0 answer

Pritipanna Ratha
Apr 17, 2014

Sin (90-0)= cos0 according to that solve..

Ashtik Mahapatra
Apr 2, 2014

Silly question

sin0=0 cos90=0

Hema Radha
Feb 3, 2014

sin 0=0 and cos 90=0 therefore answer is 0

Bill MacLaughlin
Jan 27, 2014

sin^2 0 Deg + cos^2 90 Deg ->0^2+0^2 -> 0+0-> 0

Mahedi Prince
Jan 25, 2014

it's question for little baby :p

Henry Okafor
Jan 17, 2014

s i n 2 sin^{2} 0 = 0

Also, c o s 2 cos^{2} 90 = 0

Hence the sum is 0

Ali Kaim Khani
Jan 11, 2014

SIN 0 AND COS 90 BOTH ARE ZERO THEN THE ANSWER BECOME ZERO

Shivangi Sharma
Jan 2, 2014

sin 0 = 0 cos 90 = 0 Putting these values, (0) + (0) = 0

U Z
Dec 30, 2013

sin0=0 cos0=0

soory its not cos0 its cos90

U Z - 7 years, 5 months ago
Maria Felicita
Dec 25, 2013

0 + 0 = 0

Rohan Sharma
Dec 23, 2013

since value of sin 0 and cos 90 are zero the term becomes zero

As sin 0 = 0 \sin 0^{\circ} = 0 and cos 9 0 = 0 \cos 90^{\circ} = 0 , the sum of their squares will be 0. \boxed{0.} .

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