Question

Find the angle between radius vector and tangent to the curve ​

Answer 1

• Tʜᴇ ᴛᴀɴɢᴇɴᴛ ʟɪɴᴇ ᴛᴏ ᴛʜᴇ ᴄᴜʀᴠᴇ ʀ = ғ(θ) ᴍᴀᴋᴇs ᴀɴ ᴀɴɢʟᴇ ᴏғ ψ ᴡɪᴛʜ ʀᴇsᴘᴇᴄᴛ ᴛᴏ ᴛʜᴇ ʀᴀᴅɪᴀʟ ʟɪɴᴇ ᴀᴛ ᴛʜᴇ ᴘᴏɪɴᴛ ᴏғ ᴛᴀɴɢᴇɴᴄʏ, ᴀɴᴅ ᴀɴ ᴀɴɢʟᴇ φ ᴡɪᴛʜ ʀᴇsᴘᴇᴄᴛ ᴛᴏ ᴛʜᴇ x-ᴀxɪs. Pʀᴏᴏғ: • Cᴏɴsɪᴅᴇʀ φ = θ +ψ. Tʜᴇɴ ʀ = ғ(θ) ɪs ɢɪᴠᴇɴ ɪɴ ᴘᴏʟᴀʀ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ʙʏ x = ʀᴄᴏsθ, ʏ = ʀsɪɴθ, (1) ᴡɪᴛʜ ᴀssᴏᴄɪᴀᴛᴇᴅ ᴅᴇʀɪᴠᴀᴛɪᴠᴇs ɢɪᴠᴇɴ ʙʏ.