Trig!

Geometry Level 1

Solve: Sin(45)xCos(45)xTan(45).

The above is given in degrees.


The answer is 0.5.

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2 solutions

Rakshit Pandey
Aug 13, 2014

Approach 1: We know that,
sin 4 5 o = cos 4 5 o = 1 2 \sin 45^o =\cos 45^o = \frac{1}{\sqrt 2}
and, tan 4 5 o = 1 \tan 45^o = 1
So, sin 4 5 o × cos 4 5 o × tan 4 5 o = ( 1 2 × 1 2 × 1 ) \sin 45^o \times \cos 45^o \times \tan 45^o =(\frac {1}{\sqrt 2} \times \frac {1}{\sqrt 2} \times 1)
sin 4 5 o × cos 4 5 o × tan 4 5 o = 1 2 × 2 = 1 2 = 0.5 \Rightarrow \sin 45^o \times \cos 45^o \times \tan 45^o = \frac{1}{\sqrt 2 \times \sqrt 2} =\frac{1}{2}= \boxed {0.5}


Approach 2:
sin A × cos A × tan A = sin A × cos A × sin A cos A \sin A \times \cos A \times \tan A = \sin A \times \cos A \times \frac{\sin A}{\cos A}
Cancelling cos A \cos A with the c o s A cos A in the denominator,
sin A × cos A × tan A = ( sin A ) 2 \Rightarrow \sin A \times \cos A \times \tan A = (\sin A)^2
Here A = 4 5 o A=45^o , so,
sin A × cos A × tan A = ( 1 2 ) 2 = 1 2 = 0.5 \Rightarrow \sin A \times \cos A \times \tan A = (\frac {1}{\sqrt 2})^2 = \frac{1}{2} = \boxed {0.5}

Sumit Barua
Jul 11, 2014

Sin(45)xCos(45)xTan(45)= √2/2x √2/2x1= 1/2 meaning √2/2 and √2/2 multiplies together and solve as √2x √2= 2 (numerator) and 2 multiplies 2 =4(denominator). Then ulimately divide 2/4 and multiplies by 1 = 1/2

Answer should be 0.42.

Anuj Shikarkhane - 6 years, 10 months ago

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@Jennifer Lin I've added the clarification that the values are given in degrees, as opposed to radians which would typically be the case.

Calvin Lin Staff - 6 years, 10 months ago

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