Let f(x)=sec(x) Since 58∘ is close to 60∘ and sec(60∘)=2 Also, 60∘=60×0.0175 radians =1.05 Now, f(x)=secx ⇒f′(x)=sec(x)tan(x)\f′(60∘)=sec(60∘)tan(60∘)\=2×√3=2√3 And, change in angle, ∆x=58∘−68∘=−2∘ =−2×0.0175 radians =−0.035 radians Now, ∆y≈f′(x)⋅∆x ≈2√3×(−0.035) ≈2×1.732×(−0.035) ≈−0.12124 So, sec(58∘)≈f(60∘)+∆y ⇒2−0.12124≈1.87876 So, the approximate value of sec(58∘) is 1.8788 .
