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Trigonometric Functions

Short Answer Type

21. The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of radians in the greatest angle is 60 :

straight pi

. Find the angles in degrees.

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22. Assuming the average distance of the earth from the sun to be 149,700,000 km, and the angle subtended by the sun at the eye of a person on the earth to be 32’, find the sun’s diameter.

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23. Find the angle between the minute hand of a clock and the hour hand when the time is 7:20 A.M.

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24. Find the values of other five trigonometric functions of the following:

$cosx space equals space minus 1 half comma space straight x$ lies in third quadrant

Here $space space cosx space equals space minus 1 half$

sinx<0, cosx<0, secx<0, cosecx<0, tanx>0, cotx>0 (∵ x lies in quadrant III)

Now, $sin squared straight x plus cos squared straight x space equals space 1$ $space space space rightwards double arrow space space space sin squared straight x plus 1 fourth equals 1 space space space space space space space space space space space rightwards double arrow space space space space space space space space space space sin squared straight x space equals space 3 over 4 space space space rightwards double arrow space space space sinx space equals space plus-or-minus fraction numerator square root of 3 over denominator 2 end fraction$

$rightwards double arrow$ $sinx space equals space minus fraction numerator square root of 3 over denominator 2 end fraction$ (∵ sinx is -ve)

$secx space equals space 1 over cosx space equals space minus 2$ , $cosecx space equals space 1 over sinx space equals space minus fraction numerator 2 over denominator square root of 3 end fraction comma$

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