TRIGONOMETRY.

GENERAL QUESTIONS CONCERNING TRIGONOMEFUNCTIONS.

TRICAL

1. GIVE the proper signs to sin {(2 n + 1) 180o + 0} and cos {(2n+1) 180° + 0}, supposing to be less than 90o.

2. Trace the sign of the quantity sin + cos 0, while changes from 0 to 360°.

3. If O be between 90° and 180°, what are the proper signs of sin 20, cos20, and tan20?

4. Write down a formula for all angles the tangent of which is tan 0.

5.

Write down a formula for all angles the cosine of which is 1.

=

6. Express all the trigonometrical functions in terms of the sine.

7. Express the same in terms of the tangent.

8.

The same in terms of the versedsine.

9. The same in terms of the suversedsine, (or versedsine of the supplement.)

10. If tan+cot = m, express all the trigonometrical functions in terms of m.

11. Find sin from the equation sin cos 0= m.

12.

If the right angle were divided into 100° instead of 90o, what would be the value of an angle of 36° 7′ ?

13. Determine the number of degrees into which the right angle must be divided in order that an angle of 30o may be measured by the number 40.

14. Shew that as the angle increases each of the trigonometrical functions changes sign whenever it passes through the value 0 or ∞o, and for no other value.

sin (90° + 0) = sin (90o — 0),

tantan (180° - 0) =
= − tan {(2n + 1) 180° — 0},

=

tan (180o + 0) =tan {(2n+1) 180° + 0},

cosec = cosec {(2n + 1) 180° – 0},

sec0 sec (- 0) = sec (n. 360° – ◊),

sin + cos +tan 0 sec 00,

when = 180°,

5. Give a general formula for all values of which satisfy the equation

sin n = 2 sin (n - 1)0 cos 0 sin (n − 2)0,

sin20 sin' sin (0 + p) sin (0 − p),

=

2 sec 0

2 1 + sec 0'

cos2 (0 + 4) = sin2 0 + cos o cos (20 + P),

2 (sin

sin + cos e cos3 p) = 1 + cos 20 cos 2,

cos (A+B) sin (A − B) + cos (B+ C) sin (B-C)

+ cos (C + D) sin (C – D) + cos (D + A) sin (D – A) = 0,

(90° - 0)

vers (180° - 0) = 2 vers 90o + vers 90o

sin (0 + 4) – sin 9 = sin ✪ – sin (0 – 4) – 4 sin 9 sin2 2,

Ꮎ

4 sin (0 – ) sin (m0 − p) cos (0 – m0) = 1 + cos (20 − 2m0)

-

m tan (a - 0)

then

tan (a - 20)

=

tan a.

n + m

If tan 0 = sin 20, find the value of chd 0.

5. If A, B, C, be three angles the values of which form an arithmetical progression, then

sin A - sin C: cos C-cos A :: cos B: sin B.