Solution to Chapter 3 Problems

1) Verify : 3sin(270) - 4sin(90) + 250sin(180) - 345sin(360) = -7.

                   3(-1) - 4(1) + 250(0) - 345(0) =

                            -7. 

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2) Verify : -6sin(π) + 5sin(2π) -8sin(3π/2) + 5sin(π/2) = 13.

                -6(0)  +5(0) -8(-1) +5(1) =

                            13.

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3) Verify : -23sin(3π/2)  - 20sin(π/2) + 4sin(2π) = 3.

                    -23(-1)  - 20(1) + 4(0) =

                                    3.

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4) Verify : 5cos(270) -7cos(90) + 50cos(180) -45cos(360) + 4cos(0) = -91

                    5(0)  -7(0)  +  50(-1)  -45(1)  + 4(1) = 

                                                -91.

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5) Verify : -6cos(π) + 5cos(2π) -8cos(3π/2) + 5cos(π/2) = 11.

                    -6(-1)  + 5(1)  -8(0)  +5(0) =

                                 11.

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6) Verify : -23cos(3π/2)  + 20cos(π/2) + 25cos(2π)  - cos(0) = 24.

                        -23(0)  +  20(0)   + 25(1)  - 1 =

                                                24.

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7) Verify : 5sin(270) -8cos(90) + 50tan(180) -45tan(360) + 4tan(0) = -13.

                        5(-1) -8(0)  +5(0)  -4(0)  +4(0)  =

                               -13.     

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8) Verify : -4tan(π) - 3tan(2π) -8cos(3π/2) + 5sin(π/2) = 5.

                -4(0)  - 3(0)  -8(0)  + 5(1) =

                                        5.

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9) Verify : -2tan(2π)  + 17sin(π/2) + 25tan(π)  - tan(0) = 17.

                        -2(0)   + 17(1)   +  25(0)   -=

                                            17.

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10) Verify : 2cot(270) -4cot(90) + 250cos(180) -450sin(270) = +200.

                        2(0)   -4(0)    +  250(-1)  - 450(-1)

                                                  +200.

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11) Verify : -6tan(π) + 2cos(2π) -4cot(3π/2) + 5sin(π/2) + tan(0) = 7.

                          - 6(0)  +2(1)   -4(0)  + 5(1)   + 0  =

                                                    7.

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12) Verify : -33cot(3π/2)  - 20cot(π/2) + 4tan(2π) - 3tan(0) = 0.

                            -33(0)   - 20(0)    + 4(0)  - 3(0) =

                                                      0.