Higher Engineering Mathematics, Sixth Edition

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:

1. Press sin 2. Enter 43 3. Press◦”’


2. Enter 39 5. Press◦”’ 6. Press )


3. 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:

1. Enter 6 2. Press cos 3. Enter 62


2. Press◦”’ 5. Enter 12 6. Press◦”’


3. 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 ′