1) Evaluate without using a calculator. sec ⁡ ( − π 3 ) − cot ⁡ ( − 5 π 4 )2) Evaluate without using a calculator. cos ⁡ π 2 − csc ⁡ ( − π 2 )3) Simplify the expression: tan ⁡ β cot ⁡ β4) Evaluate without using a calculator. sin 2 ⁡ 20 ∘ + 1 sec 2 ⁡ 20 ∘ 5) Evaluate without using a calculator. sin ⁡ ( − 40 ∘ ) cos ⁡ 50 ∘ 6) Evaluate without using a calculator. sin ⁡ 400 ∘ sec ⁡ ( − 50 ∘ )7) Find the exact value of all remaining trig functions sin ⁡ θ = 4 5 , θ is acute

Question

1) Evaluate without using a calculator.  sec  ⁡  (  −      π    3    )  −  cot  ⁡  (  −            5      π        4    )2) Evaluate without using a calculator.  cos  ⁡      π    2    −  csc  ⁡  (  −      π    2    )3) Simplify the expression:  tan  ⁡  β  cot  ⁡  β4) Evaluate without using a calculator.      sin          2        ⁡      20          ∘        +      1                  sec                  2                    ⁡              20                  ∘                    5) Evaluate without using a calculator.            sin      ⁡      (      −              40                  ∘                    )              cos      ⁡              50                  ∘                    6) Evaluate without using a calculator.  sin  ⁡      400          ∘        sec  ⁡  (  −      50          ∘        )7) Find the exact value of all remaining trig functions  sin  ⁡  θ  =      4    5    ,  θ is acute

gutsy8v · Accepted Answer

Step 11)   sec  ⁡  (  −            −      π        3    )  −  cot  ⁡  (  −            5      π        4    )  =  sec  ⁡  (      π    3    )  +  cot  ⁡  (            5      π        4    )  =  2  +  1  =  3Step 22)   cos  ⁡  (      π    2    )  −  csc  ⁡  (  −      π    2    )  =  cos  ⁡  (      π    2    )  +  csc  ⁡  (      π    2    )  =  0  +  1  =  1Step 33)   tan  ⁡  β  cot  ⁡  β  =  tan  ⁡  β  ⋅      1          tan      ⁡      β        =  1Step 44)       sin          2        ⁡  20  +      1                  sec                  2                    ⁡      20        =      sin          2        ⁡  20  +      cos          2        ⁡  20  =  1Step 55)             sin      ⁡      (      −      40      )              cos      ⁡      50        =            −      sin      ⁡      (      40      )              cos      ⁡      (      90      −      40      )        =            −      sin      ⁡      40              sin      ⁡      40        =  −  1Step 66)   sin  ⁡  400  sec  ⁡  (  −  50  )  =  sin  ⁡  (  360  +  40  )  sec  ⁡  (  50  )  =            sin      ⁡      40              cos      ⁡      50        =            cos      ⁡      50              cos      ⁡      50        =  1Step 77)   sin  ⁡  θ  =      4    5      p  =  4  ,  h  =  5    b  =            h      2        −          b      2        =            5      2        −          4      2        =    3      cos  ⁡  θ  =      b    h    =      3    5      tan  ⁡  θ  =      p    b    =      4    3      csc  ⁡  θ  =      5    4      sec  ⁡  θ  =      5    3      cot  ⁡  θ  =      3    4

Evaluate without using a calculator. sec(-\pi/3)-cot(-(5\pi)/4)=sec(\pi/3)+cot((5\pi)/4)=2+1=3

Answered question

Answer & Explanation

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