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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

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

$sinx space equals space 3 over 5 comma space straight x$ lies in second quadrant

Here, sinx = $3 over 5$

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

Now,    $sin squared straight x plus cos squared straight x space equals space 1 space space space space rightwards double arrow space space space space space space 9 over 25 plus cos squared straight x space equals space 1 space space space rightwards double arrow space space space space cos squared straight x space equals space 16 over 25 space space space space rightwards double arrow space space space cosx space equals space plus-or-minus 4 over 5$

$rightwards double arrow$    $cosx space equals space minus 4 over 5$ (∵ cosx is -ve)

$cosecx space equals space 1 over sinx space equals space 5 over 3 comma space$    $secx space equals space 1 over cosx space equals space minus 5 over 4$

   $tanx space equals space sinx over cosx space equals space minus 3 over 4 comma$    $cotx space equals space cosx over sinx space equals space minus 4 over 3$