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Grace [21]
4 years ago
11

Which of the following trigonometric expressions is equivalent to csc(-112°)? csc(68°)

Mathematics
2 answers:
amid [387]4 years ago
7 0

Answer:

Step-by-step explanation:

To find: \csc \left ( -112^{\circ} \right )

Solution:

Trigonometric expression is an expression consisting of trigonometric ratios like \sin ,\tan ,\cos ,\csc ,\cot ,\sec

Trigonometric ratios refers to the relation between the sides of right angled triangle and it's angles.

We know that angle -112^{\circ} lies in the fourth quadrant in which \csc is negative

So, \csc \left ( -112^{\circ} \right )=-\csc \left ( 112^{\circ} \right )

We can write -\csc \left ( 112^{\circ} \right )=-\csc \left ( 180^{\circ}-68^{\circ} \right )

We know that angle 180^{\circ}-68^{\circ}=112^{\circ} lies in second quadrant in which \csc is positive

-\csc \left ( 180^{\circ}-68^{\circ} \right )=-\csc68^{\circ}

Therefore, we get

\csc(-112^{\circ})=-\csc(112^{\circ})=-\csc \left ( 180^{\circ}-68^{\circ} \right )=-\csc68^{\circ}

Romashka-Z-Leto [24]4 years ago
4 0

Answer:

csc(-112°)=-csc(68°)

Step-by-step explanation:

Since cosec(x) and sin(x) are reciprocals of each other,

cosec(-112°)=\frac{1}{sin(-112^{\circ})}

                  =\frac{1}{-sin(112^{\circ})}

                 =\frac{1}{-sin(180^{\circ}-68^{\circ})}     (since 112=180-68)

                 =\frac{1}{-sin(68^{\circ})}              (since sin(180-x)=sinx)

                 =\frac{-1}{sin(68^{\circ})}               (since \frac{a}{-b}= \frac{-a}{b})

                 =-cosec(68°)

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