If sin of theta equals 3/8 and theta is in quadrant II. what are cos, tan, csc, cot, and sec of theta?

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kizintefevd3 · Accepted Answer

sin      θ        =          3      8      By rearranging the Pythagorean theorem, we can calculate the adjacent side, b, since we already have the side opposite to       θ  ,       3  , and the hypotenuse,       8  .            a      2        +          b      2        =          c      2                  b      2        =          c      2        -          a      2                  b      2        =          8      2        -          3      2                  b      2        =    64    -    9              b      2        =    55        b    =    -                  55            From this, we can determine that the side that is next to it has a length of       -                  55             units, since the x-axis is negative in the second quadrant. Therefore, we can infer that             cos      θ        =    -                            55                    8       and             tan      θ        =    -          3                                    55                              Now, using the reciprocal identities, we must take the reciprocals of forces, sine, and cosine.            csc      θ        =          1              sin        θ                        sec      θ        =          1              cos        θ                        cot      θ        =          1              tan        θ            So,             csc      θ        =          8      3        ,          sec      θ        =    -          8                        55                                  and                    cot      θ        =    -                            55                    3      In conclusion, the six trigonometric ratios are:            sin      θ        =          3      8                  cos      θ        =    -                            55                    8                  tan      θ        =    -          3                        55                                csc      θ        =          8      3                  sec      θ        =    -          8                        55                                cot      θ        =    -                            55                    3

Nhluvukoj6m · Accepted Answer

sin      θ        =          3      8        →          (                        1                    )            •          csc      θ        =          1              sin        θ              =          8      3        →          (                        2                    )            •          cos      θ        =    ±                  1        -                              sin            2                    θ                                        ×        ×        x              =    -                  1        -                  9          64                                                               ×        ×        x              =    -                            55          64                          ⇒          cos      θ        =    -                  55            8        →          (                        3                    )            •          sec      θ        =          1              cos        θ              =    -          8              55              →          (                        4                    )            •          sec      θ        =          1              cos        θ              =    -          8              55              →          (                        4                    )            •          tan      θ        =                            sin          θ                                      cos          θ                                        ×        ×              =          3      8        ×    -          8              55              =    -          3              55              →          (                        5                    )            •          cot      θ        =          1              tan        θ              =    -                  55            3        →          (                        6                    )

If sin of theta equals 3/8 and theta is in quadrant II. what are cos, tan, csc, cot, and sec of theta?

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