Introduction to trigonometry 101
values, correct to 4 decimal places, may be checked:
secant 32◦=
1
cos32◦
= 1. 1792
cosecant 75◦=
1
sin75◦
= 1. 0353
cotangent41◦=
1
tan41◦
= 1. 1504
secant 215. 12 ◦=
1
cos215. 12 ◦
=− 1. 2226
cosecant 321. 62 ◦=
1
sin321. 62 ◦
=− 1. 6106
cotangent263. 59 ◦=
1
tan263. 59 ◦
= 0. 1123
If we know the value of a trigonometric ratio and need
to find the angle we use theinverse functionon our
calculators.
For example, using shift and sin on our calculator gives
sin−^1 (
If, for example, we know the sine of an angle is 0.5 then
the value of the angle is given by:
sin−^10. 5 = 30 ◦ (Check that sin30◦= 0. 5 )
(Note that sin−^1 xdoes not meansin^1 x;also,sin−^1 xmay
also be written as arcsinx)
Similarly, if cosθ= 0 .4371 then
θ=cos−^10. 4371 = 64. 08 ◦
and if tanA= 3 .5984 thenA=tan−^13. 5984
= 74. 47 ◦
each correct to 2 decimal places.
Use your calculator to check the following worked
examples.
Problem 6. Determine, correct to 4 decimal
places, sin43◦ 39 ′
sin43◦ 39 ′=sin43
39
60
◦
=sin43. 65 ◦
= 0. 6903
This answer can be obtained using thecalculatoras
follows:
- Press sin 2. Enter 43 3. Press◦”’
- Enter 39 5. Press◦”’ 6. Press )
- Press= Answer=0.6902512....
Problem 7. Determine, correct to 3 decimal
places, 6cos62◦ 12 ′
6cos62◦ 12 ′=6cos62
12 ◦
60
=6cos62. 20 ◦
= 2. 798
This answer can be obtained using thecalculatoras
follows:
- Enter 6 2. Press cos 3. Enter 62
- Press◦”’ 5. Enter 12 6. Press◦”’
- Press) 8. Press= Answer=2.798319....
Problem 8. Evaluate correct to 4 decimal places:
(a) sine168◦ 14 ′ (b) cosine271. 41 ◦
(c) tangent98◦ 4 ′
(a) sine168◦ 14 ′=sine168
14 ◦
60
=0.2039
(b) cosine271. 41 ◦=0.0246
(c) tangent98◦ 4 ′=tan98
4 ◦
60
=−7.0558
Problem 9. Evaluate, correct to 4 decimal places:
(a) secant 161◦ (b) secant 302◦ 29 ′
(a) sec161◦=
1
cos161◦
=−1.0576
(b) sec302◦ 29 ′=
1
cos302◦ 29 ′
=
1
cos302
29 ◦
60
=1.8620
Problem 10. Evaluate, correct to 4 significant
figures:
(a) cosecant 279. 16 ◦ (b) cosecant 49◦ 7 ′
(a) cosec 279. 16 ◦=
1
sin279. 16 ◦
=−1.013
(b) cosec 49◦ 7 ′=
1
sin49◦ 7 ′
=
1
sin49
7 ◦
60
=1.323
Problem 11. Evaluate, correct to 4 decimal
places:
(a) cotangent17. 49 ◦ (b) cotangent163◦ 52 ′